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arXiv · 2403.09711

Two-dimensional generalized gamma function and its applications

Artem M. Ponomarenko
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Abstract

In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later, this generalization is also a generalization the famous formula that gives the connection between the classical gamma and beta functions. Next we present properties of this generalization, some series for the generalized beta function. As a practical application of the two-dimensional generalized gamma function, we will show how it can be used to represent a fairly wide class of double integrals in the form of functional series.

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Artem M. Ponomarenko. 2024-03-10. Two-dimensional generalized gamma function and its applications. https://arxiv.org/abs/2403.09711

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